Problem: $\left(-10x + 1\right)^2 = \ ?$
Explanation: $= \left(-10x + 1\right)\left(-10x + 1\right)$ $= -10x \cdot \left(-10x + 1\right) + 1 \cdot \left(-10x + 1\right)$ $= \left( -10x \cdot -10x \right) + \left( -10x \cdot 1 \right) + \left( 1 \cdot -10x \right) + \left( 1 \cdot 1 \right)$ $= 100x^2 + \left( -10x \cdot 1 \right) + \left( 1 \cdot -10x \right) + \left( 1 \cdot 1 \right)$ $= 100x^2 + \left( -10x - 10x \right) + \left( 1 \cdot 1 \right)$ $= 100x^2 - 20x + \left( 1 \cdot 1 \right)$ $= 100x^2 - 20x + 1$